Divide the following complex numbers: $\dfrac{4(\cos(\frac{23}{12}\pi) + i \sin(\frac{23}{12}\pi))}{\cos(\frac{5}{6}\pi) + i \sin(\frac{5}{6}\pi)}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.) Re Im
Solution: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $4(\cos(\frac{23}{12}\pi) + i \sin(\frac{23}{12}\pi))$ ) has angle $\frac{23}{12}\pi$ and radius 4. The second number ( $\cos(\frac{5}{6}\pi) + i \sin(\frac{5}{6}\pi)$ ) has angle $\frac{5}{6}\pi$ and radius 1. The radius of the result will be $\frac{4}{1}$ , which is 4. The angle of the result is $\frac{23}{12}\pi - \frac{5}{6}\pi = \frac{13}{12}\pi$ The radius of the result is $4$ and the angle of the result is $\frac{13}{12}\pi$.